If they stop short of a weekly music show on BBC1, eight years after the demise of Top of the Pops (a brand since tarnished by Savile), then Shennan does not want for ambition. "I'd like to think we could come up with a proposal for BBC1 which would make doing something on music really attractive," he says. "When they did the [Diamond] Jubilee concert from Buckingham Palace, that was a massive hit. I'm looking at projects that will have impact."

Tasked by BBC director general Tony Hall with building BBC Music into a brand with the cachet of BBC News or BBC Sport, Shennan says the BBC's various music services and departments are not yet the sum of their parts, only coming together for big events like Glastonbury. "We should be making more of the fact we have BBC1, Radio 2, Radio 1; these are huge music-friendly vehicles and I'd love to find ways for these services to work together. I imagine if ITV had Radio 1 and Radio 2 they would probably have found a way of making them all connect at some point."

The BBC has been criticised for not doing more regular TV music programmes outside of Later … with Jools Holland on BBC2. Shennan will look to tackle this with a BBC Music brand visible to viewers for the first time at Glastonbury, and will embrace a whole range of content on the BBC's iPlayer. He does so from a position of strength, Radio 2 having just recorded its biggest ever audience of 15.6 million listeners a week, and been named station of the year at this month's Radio Academy Awards.

It capped an extraordinary transformation for the station – from pipe and slippers to modern mainstream – in the last decade and a half, beginning with the hiring of Jonathan Ross. Shennan took charge in 2009, steadying the ship in the wake of the "Sachsgate" scandal (Ross again) and overseeing the potentially tricky transition from Sir Terry Wogan to Chris Evans at breakfast.

In the event, Evans is even more popular than his predecessor, his three-hour show has nearly 10 million listeners each week.As well as Evans, Shennan says Graham Norton has had a "significant impact" in Ross's old Saturday morning slot, with a record 4.3 million listeners. "There's something about society that needs Radio 2 just now," says Shennan. "We often find ourselves criticised for sounding too old and safe, or pushing too young, and the reality is we are neither. Middle age is the new young, we are all aspiring to stay young, and that's why Radio 2 cleans up."

But there appears to be substance to the criticism. Some 2.7 million of Radio 2's listeners are under 35, despite the station's remit, set by the BBC Trust, to target over-35s. Shennan responds by saying the number of over-55s listening to the station, at 6.7 million, is at a record high. "A little bit like certain other radio stations [Radio 1, which is trying to shed its older audience], it's impossible to tell people not to listen to you," he argues. "Prince is 55. Are we not catering for somebody who is the same age as Prince? Of course we are."

But while the average age of the Radio 2 listener remains 51, he admits that some over-75s may have switched off, particularly on Sunday nights, where he introduced a new Michael Ball show in an attempt to stem declining ratings. "We've done some things to the schedule which have alienated those people and that concerns me," says Shennan. "That's simply because around 75 there is a switch in musical taste, mainstream popular music post-Beatles is far less attractive to that audience."

Presenter Russell Davies, whose Sunday night show featuring Cole Porter and Irving Berlin was dropped last year, accused the network of axing DJs "who know anything before the Beatles". Shennan says: "It's wrong just to preside over steep decline. You have to do something about it."

The station has also been criticised for its all-male weekday daytime line-up, from Evans at breakfast until Jo Whiley's evening show begins at 8pm. Shennan has introduced Zoe Ball, Sara Cox and Vanessa Feltz to the station – along with Whiley – but they remain outside of peak time or deputise for the main presenters. "I understand why people think it's an anomaly but there has been no shortage of change on the station since 2008 and those [male] daytime presenters keep becoming more and more popular," he argues. "We are there to serve the audience and the audience loves those programmes." Shennan does not guarantee a woman will succeed whichever daytime DJ leaves first, but says he will choose from "the broadest possible selection of talent".

Shennan, a former controller of Radio 5 Live whose only stint away from the BBC was at ill-fated Channel 4 Radio, was widely tipped to succeed Tim Davie in the BBC's top radio job. But when Davie went to BBC Worldwide, via a few months as acting director general, the job went to Helen Boaden, moved sideways out of BBC News last year in the wake of the Savile scandal.

Shennan says he was not interviewed for the job "and I didn't apply for it because I don't think it was advertised. When I heard what was happening I thought it made great sense. I work very well with Helen." And anyway, he says, he is "enormously excited" by the director of music job for which he will receive a pay rise (on top of the £223,000 he already earns), and which was not advertised either.

As the BBC's director of music, does he know what's number one in the singles charts? No, it turns out (it was Rita Ora, I Will Never Let You Down). A fair question? "No, because that's about Radio 1 and Ben [Cooper] is the one who looks after Radio 1," says Shennan. "This job I've got is a strategic job, it's about leading music for the BBC."

Shennan, a country music fan who also counts Bob Dylan, Coldplay and Elbow among his favourites, oversees digital station, Radio 6 Music, as well as the Asian Network. 6 Music, almost axed in 2010, now has nearly 2 million listeners, just as Shennan predicted three years ago. It can grow further, he says, even up to 3 million.

But 6 Music's budget has been cut by around a quarter, to £4m (in terms of what Shennan spends on programmes) with Radio 2's budget cut by a similar proportion, to £15m by 2016 from £20m in 2011, as part of BBC cutbacks. The Asian Network will lose 50%.

Shennan's new role, which reflects a similar BBC drive in the arts, will mean extra money for music, but the amount is not expected to be substantial. He will chair a steering group including Radio 1's Cooper, Jan Younghusband, head of commissioning, BBC music and events TV, and head of music television Mark Cooper, who heads up in-house production.

Everyone's first question, Shennan says, is about Top of the Pops, but a regular BBC1 music show looks off the menu. "I do think there are things we can do – in the end my colleagues in television are the ultimate arbiters – to do more high-impact content on TV. As resources have become more pressurised, everything we do has to have impact."